Design a cam using polynomials with the following specificat

Design a cam (using polynomials) with the following specifications:

Accelerate the follower from 0 to 0.01 in/deg^2 in 30 degree of cam rotation

Hold a constant acceleration of 0.01 in/deg^2 for 60 degree

Decelerate to a=0 in the next 90 degree

The displacement and velocity should be at zero at a cam angle of a 0 at 180 degree

Dwell at s=0 from 180 to 360 degree

a) Determine the s polynomials that will satisfy the constrains for cam angle from 0 to 30 degree

b) Determine the s polynomials that will satisfy the constrains for cam angle from 30 to 90 degree

Solution

Given:

Velocity @ each end is zero

Acceleration is constant till 30⁰ A

Acceleration zero from 30 to 60⁰

Deceleration constant from 60 to 90⁰

Dwell is from 180 to 360⁰

As deceleration reaches to zero @ 90⁰ & we assume dwell period from 90 to 3600.Taking an account of Rise-Dwell-Return-Dwell profile

‘a₁ = 0.1 in/s²

= .1 x 12.5 mm/s²

= 0.125 mm/s² = a₂ (acceleration for 60⁰)

At Rise (from 0 to 30⁰)

Motion of follower is linear so equation will be

S = a₁t + a₀

S= .125 t

Velocity @ this point will be

V_max = (0.5) x H (/)

‘a_max = (0.5) x H [(/)]²

At Return (from 60 to 90⁰)

V_max = 4 H/ (1 -/)

‘a_max = 4 x H [/)]²